The Local Moduli of Sasakian 3-Manifolds

Details The Local Moduli of Sasakian 3-Manifolds The Local Moduli of Sasakian 3-Manifolds

2001-02-02

arxiv.org/abs/math/0102015v1

Int. J. Math. Sci. 32 (2002) 117-127.

Mathematics

Differential Geometry

9 pages, RevTeX, no figures

Scientific paper

The Newman-Penrose-Perjes formalism is applied to Sasakian 3-manifolds and the local form of the metric and contact structure is presented. The local moduli space can be parameterised by a single function of two variables and it is shown that, given any smooth function of two variables, there exists locally a Sasakian structure with scalar curvature equal to this function. The case where the scalar curvature is constant ($\eta$-Einstein Sasakian metrics) is completely solved locally. The resulting Sasakian manifolds include $S^3$, $Nil$ and $\tilde{SL_2R}$, as well as the Berger spheres. It is also shown that a conformally flat Sasakian 3-manifold is Einstein of positive scalar curvature.

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